铝型材壁板挤压模具结构优化设计研究
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摘要
大型整体铝合金壁板因其具有比强度高、耐蚀性和气密性好、造型美观等优点,在铁路、航空、船舶等交通运输业中的应用越来越广泛,其成形过程主要用扁挤压筒挤压方法来完成。挤压模具的型腔形状在成形过程中至关重要,其与工件的变形程度、变形速度、塑性变形区的应力状态等密切相关,对成形件质量、挤压能耗和模具寿命等有十分重要的影响。本文围绕大型复杂壁板挤压模具型腔优化,综合运用数学、流体力学、数值模拟和物理模拟等知识,对壁板挤压成形规律进行深入研究,完成壁板挤压模具型腔的优化设计,取得了一些有重要意义的结论和对实际应用有指导作用的成果。
首先基于复变函数共形映射原理,把映射函——Schwarz-Christoffel积分,从物理学、电磁学应用领域,引入到塑性加工过程分析中,将挤压入口、出口多边形形状映射到一单位圆周上,提出复杂型材挤压模具型腔映射建模思路。完整推导了Schwarz-Christoffel积分的两步求解过程,针对映射精度问题,提出凸凹分级展开求解技术,借助MATLAB平台,开发许氏积分快速求解模块。在实现简单多边形与单位圆映射函数求解的基础上,利用该积分完成复杂多边形壁板(矩形、梯形、工字形)与单位圆之间映射函数的求解,将复杂多边形问题转化为单位圆问题。
根据上限理论,建立铝合金圆棒料挤压成形的流动模型,推导坯料在五种不同形状型腔下变形时的动可容速度场、应变速率场及上限功率的表达式。以降低挤压能耗为优化目标,对成形过程进行优化,获得最低能耗下的型腔高度。在此基础上,结合流体力学理论,引入流函数方程,建立基于流曲线的壁板挤压过渡曲面边界条件,得到挤压模具型腔“流线型”数学模型,完成复杂截面壁板型材挤压的“流线型”过渡曲面建模。
借助数值模拟软件,采用二维弹塑性和三维刚塑性有限元方法分别对铝合金棒料及复杂壁板挤压过程进行模拟,验证不同模具型腔对挤压过程的影响,获得材料成形时金属位移场、速度场、应力-应变场和温度场的分布情况。深入分析壁板成形时的金属流动规律。此外,选取挤压中心等与挤压过程密切关联的因素,讨论其对挤压过程的影响,获得了一些有用的结果。研究发现,相同断面缩减率下,流线型型腔在改善金属流动、降低成形载荷和提高制件质量上都存在较大优势。
由于生产壁板的重要工具扁挤压筒要在高温、高压、高摩擦的恶劣条件下工作,其使用寿命较低,这里引入混合优化方法,对扁挤压筒进行结构优化设计,将有限元法(FEM)、人工神经网络(ANN)和多目标遗传算法(MOGA)运用到扁挤压筒结构优化中,综合考虑扁挤压简最佳工作性能和内腔的尺寸精度,建立变过盈量下三层组合式扁挤压筒结构的多目标优化模型,获得满足约束条件下的扁挤压筒各层结构参数。同时,以梯形铝合金壁板挤压成形为例,结合试验设计(DOE)、响应面设计(RSM)和遗传模拟退火算法(GSA),从降低成形载荷和提高壁板质量角度,对影响挤压过程的重要工艺参数——挤压速度v、定径带长度l、模具温度T_1等进行多目标优化设计,获得满足条件下的最佳成形工艺参数。
最后采用光塑性试验方法分析了梯形壁板“流线型”挤压成形过程,实验获得光塑性模型材料最佳的成形温度及合理的材料热处理规范。通过对模型切片的分析,得到模型中应变分量的分布规律,试验结果与模拟结果相吻合,从而验证了“流线型”模具型腔在壁板挤压过程中的优越性。
本文的研究成果,可以为复杂截面铝合金型材挤压生产提供技术支持,对于完善壁板挤压模具设计理论具有实际指导意义。
Large-sized aluminum alloy flat-plate, with some characteristics like high specific strength, corrosion resistance, unfailing performance and attractive appearance, has been widely used in railway transportation, air transportation, ship transportation and so on. It is usually formed through extruding by combined flat container. Thus the die cavity is very important for forming process, which is closely related to deformation degree, forming velocity, stress states in deforming area, and has a great influence on the products quality, extrusion energy and die life. In this dissertation, the optimization of die cavity structure is carried out by comprehensive application of mathematics, fluid mechanics, numerical simulation and physical simulation. Through the research, the extrusion forming discipline of flat-plate is got, and some useful conclusions and instructional achievements are obtained.
According to conformal mapping theory of complex function, the mapping function of Schwarz-Christoffel integral is introduced from physics field, electromagnetics field to plastic forming process. By this function, the extrusion inlet and outlet are mapped to a unit circle, and then the mapping modeling approach is put forward. First, the forward and reverse solution procedure for Schwarz-Christoffel integral is analyzed. Handling the problem of mapping accuracy, the convex-concave expansion technology for Taylor series expansion is adopted. To improve the solution efficiency, the fast-solution mode is developed on the MATLAB platform. By this mode, the mapping function from a simple polygon to a unit circle can be acquired quickly, and other complicated mapping functions from rectangle, trapezoid, I-section polygon to unit circle can also be solved accurately.
Based on the upper bound theory, the flowing model for aluminum alloy rod extrusion is constructed, and then the kinematically admissible velocity field, the strain rate field and the deformation power are deduced with five different die containers. In addition, aiming at reducing extrusion power, the forming process optimization is carried out, from which the best container length with the less extrusion load is got. According to this, the boundary condition of transitional surface between flat extrusion container cavity and die outlet is established based on the flow function method, then the streamlined mathematic model of die cavity is constructed, and the streamlined 3D model of transitional surface is obtained by using CAD software.
In order to verify the influence of different die cavity on extrusion process, the forming process of aluminum rod and complicated flat-plate extrusion are simulated by 2D elastic-plastic FEM and 3D rigid-plastic FEM respectively. Through the simulation, the displacement field, velocity field, stress-strain field and temperature field distribution discipline in forming process are obtained. In addition, some important factors that connected to forming process, such as the extrusion center etc, are discussed. The simulation results show, with the same area reduction ratio, streamlined cavity has great advantages in improving metal flowing, reducing forming load and enhancing products quality.
Furthermore, flat extrusion container is working with the environment of high temperature, high pressure and high friction, which leads to the poor operating life. The hybrid optimization method, combining finite element method (FEM), artificial neural network (ANN), multi-objective genetic algorithm (MOGA) together, is adopted to optimize the container structure. Considering the strength of flat extrusion container and dimensional accuracy of inner layer, the multi-objective structural optimization of three-layer combined flat extrusion container under the non-uniform shrinkage design is realized. With analyzing, comparing and demonstrating, a feasible method of structural optimum design for flat extrusion container is obtained. Meanwhile, in order to reduce extrusion power and improve flat-plate quality, the important forming parameters, including extrusion velocity, calibrating length, die temperature and so on, are optimized with the combination of orthogonal experimental design, response surface method (RSM) and genetic simulated annealing algorithm (GSA). From this multi-objective optimization, the best procedure parameters are obtained.
In the last, the streamlined extrusion process of trapezoid flat-plate is analyzed by photo-plasticity method. Based on the experiments, the best forming temperature and the reasonable heat treatment regime for experimental material are acquired. By the analysis of product sections, the strain distribution discipline along different path in the parts is got. And there is little difference between experimental and simulation results, thus it can prove the advantage of streamlined die cavity in extrusion process.
Our results will have significant reference to extruding die design for flat-plate, and it can provide technical supports for other complicated flat-plate forming.
首先基于复变函数共形映射原理,把映射函——Schwarz-Christoffel积分,从物理学、电磁学应用领域,引入到塑性加工过程分析中,将挤压入口、出口多边形形状映射到一单位圆周上,提出复杂型材挤压模具型腔映射建模思路。完整推导了Schwarz-Christoffel积分的两步求解过程,针对映射精度问题,提出凸凹分级展开求解技术,借助MATLAB平台,开发许氏积分快速求解模块。在实现简单多边形与单位圆映射函数求解的基础上,利用该积分完成复杂多边形壁板(矩形、梯形、工字形)与单位圆之间映射函数的求解,将复杂多边形问题转化为单位圆问题。
根据上限理论,建立铝合金圆棒料挤压成形的流动模型,推导坯料在五种不同形状型腔下变形时的动可容速度场、应变速率场及上限功率的表达式。以降低挤压能耗为优化目标,对成形过程进行优化,获得最低能耗下的型腔高度。在此基础上,结合流体力学理论,引入流函数方程,建立基于流曲线的壁板挤压过渡曲面边界条件,得到挤压模具型腔“流线型”数学模型,完成复杂截面壁板型材挤压的“流线型”过渡曲面建模。
借助数值模拟软件,采用二维弹塑性和三维刚塑性有限元方法分别对铝合金棒料及复杂壁板挤压过程进行模拟,验证不同模具型腔对挤压过程的影响,获得材料成形时金属位移场、速度场、应力-应变场和温度场的分布情况。深入分析壁板成形时的金属流动规律。此外,选取挤压中心等与挤压过程密切关联的因素,讨论其对挤压过程的影响,获得了一些有用的结果。研究发现,相同断面缩减率下,流线型型腔在改善金属流动、降低成形载荷和提高制件质量上都存在较大优势。
由于生产壁板的重要工具扁挤压筒要在高温、高压、高摩擦的恶劣条件下工作,其使用寿命较低,这里引入混合优化方法,对扁挤压筒进行结构优化设计,将有限元法(FEM)、人工神经网络(ANN)和多目标遗传算法(MOGA)运用到扁挤压筒结构优化中,综合考虑扁挤压简最佳工作性能和内腔的尺寸精度,建立变过盈量下三层组合式扁挤压筒结构的多目标优化模型,获得满足约束条件下的扁挤压筒各层结构参数。同时,以梯形铝合金壁板挤压成形为例,结合试验设计(DOE)、响应面设计(RSM)和遗传模拟退火算法(GSA),从降低成形载荷和提高壁板质量角度,对影响挤压过程的重要工艺参数——挤压速度v、定径带长度l、模具温度T_1等进行多目标优化设计,获得满足条件下的最佳成形工艺参数。
最后采用光塑性试验方法分析了梯形壁板“流线型”挤压成形过程,实验获得光塑性模型材料最佳的成形温度及合理的材料热处理规范。通过对模型切片的分析,得到模型中应变分量的分布规律,试验结果与模拟结果相吻合,从而验证了“流线型”模具型腔在壁板挤压过程中的优越性。
本文的研究成果,可以为复杂截面铝合金型材挤压生产提供技术支持,对于完善壁板挤压模具设计理论具有实际指导意义。
Large-sized aluminum alloy flat-plate, with some characteristics like high specific strength, corrosion resistance, unfailing performance and attractive appearance, has been widely used in railway transportation, air transportation, ship transportation and so on. It is usually formed through extruding by combined flat container. Thus the die cavity is very important for forming process, which is closely related to deformation degree, forming velocity, stress states in deforming area, and has a great influence on the products quality, extrusion energy and die life. In this dissertation, the optimization of die cavity structure is carried out by comprehensive application of mathematics, fluid mechanics, numerical simulation and physical simulation. Through the research, the extrusion forming discipline of flat-plate is got, and some useful conclusions and instructional achievements are obtained.
According to conformal mapping theory of complex function, the mapping function of Schwarz-Christoffel integral is introduced from physics field, electromagnetics field to plastic forming process. By this function, the extrusion inlet and outlet are mapped to a unit circle, and then the mapping modeling approach is put forward. First, the forward and reverse solution procedure for Schwarz-Christoffel integral is analyzed. Handling the problem of mapping accuracy, the convex-concave expansion technology for Taylor series expansion is adopted. To improve the solution efficiency, the fast-solution mode is developed on the MATLAB platform. By this mode, the mapping function from a simple polygon to a unit circle can be acquired quickly, and other complicated mapping functions from rectangle, trapezoid, I-section polygon to unit circle can also be solved accurately.
Based on the upper bound theory, the flowing model for aluminum alloy rod extrusion is constructed, and then the kinematically admissible velocity field, the strain rate field and the deformation power are deduced with five different die containers. In addition, aiming at reducing extrusion power, the forming process optimization is carried out, from which the best container length with the less extrusion load is got. According to this, the boundary condition of transitional surface between flat extrusion container cavity and die outlet is established based on the flow function method, then the streamlined mathematic model of die cavity is constructed, and the streamlined 3D model of transitional surface is obtained by using CAD software.
In order to verify the influence of different die cavity on extrusion process, the forming process of aluminum rod and complicated flat-plate extrusion are simulated by 2D elastic-plastic FEM and 3D rigid-plastic FEM respectively. Through the simulation, the displacement field, velocity field, stress-strain field and temperature field distribution discipline in forming process are obtained. In addition, some important factors that connected to forming process, such as the extrusion center etc, are discussed. The simulation results show, with the same area reduction ratio, streamlined cavity has great advantages in improving metal flowing, reducing forming load and enhancing products quality.
Furthermore, flat extrusion container is working with the environment of high temperature, high pressure and high friction, which leads to the poor operating life. The hybrid optimization method, combining finite element method (FEM), artificial neural network (ANN), multi-objective genetic algorithm (MOGA) together, is adopted to optimize the container structure. Considering the strength of flat extrusion container and dimensional accuracy of inner layer, the multi-objective structural optimization of three-layer combined flat extrusion container under the non-uniform shrinkage design is realized. With analyzing, comparing and demonstrating, a feasible method of structural optimum design for flat extrusion container is obtained. Meanwhile, in order to reduce extrusion power and improve flat-plate quality, the important forming parameters, including extrusion velocity, calibrating length, die temperature and so on, are optimized with the combination of orthogonal experimental design, response surface method (RSM) and genetic simulated annealing algorithm (GSA). From this multi-objective optimization, the best procedure parameters are obtained.
In the last, the streamlined extrusion process of trapezoid flat-plate is analyzed by photo-plasticity method. Based on the experiments, the best forming temperature and the reasonable heat treatment regime for experimental material are acquired. By the analysis of product sections, the strain distribution discipline along different path in the parts is got. And there is little difference between experimental and simulation results, thus it can prove the advantage of streamlined die cavity in extrusion process.
Our results will have significant reference to extruding die design for flat-plate, and it can provide technical supports for other complicated flat-plate forming.
引文
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